This is an open-label, dose and regimen escalation study of CP-358,774, a novel anti-cancer agent which inhibits epidermal growth factor receptor (EGFR) tyrosine kinase actvity and thus inhibits the growth of human EGFR-expressing tumors. The purpose of the study is to evluate the safety, toleration, pharmacokinetics and maximum tolerated dose of daily administration of CP-358,774 to patients with advanced cancers. A secondary objective of the study is to evaluate the anti-tumor activity of daily dosing of the study drug, using validated clinical endpoints. The study has three sequential treatment legs incorporating different frequencies of administration.